Question

The figure below shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced:

Triangle ABC has length of BC equal to 16 inches. A line segment DC joins the point D on AB with point C. Measure of angle ABC is 90 degrees, ACD is 15 degrees and measure of angle DCB is 30 degrees.

What is the length of the wood that is needed to replace AD?

Answer 1

@stacy.reed08

Answer 2

6.8 inches
6.2 inches
3.2 inches
2.8 inches

Answer 3

I thought maybe doing 15 divided by 2 would work but i got 7.5 inches and thats not an option so im assuming there's a step im missing

Answer 4

I should have looked down at the picture...it took me forever to draw by hand.

Answer 5

ok, so if you think about it, there is a little triangle inside the larger triangle ABC

Answer 6

Yes i see that

Answer 7

ok, let's draw that triangle out separately

Answer 8

I take that back...sorry, I thought we were trying to figure out line segment DC...just kidding, we want AD

Answer 9

im guessing in order to find out the rotting piece needed to be replaced we have to find out how long side CD is?

Answer 10

ok, I know the answer and there is probably an easier way to get there, but this is what makes sense in my mind...

Answer 11

use the smaller triangle to figure out the length of DB.

Answer 12

How do we do that

Answer 13

OH